Connectome Smoothing via Low-rank Approximations

TL;DR

This paper introduces a low-rank approximation method for estimating the mean of brain network graphs, improving accuracy especially with small samples by exploiting structural properties.

Contribution

It proposes a low-rank smoothing technique with dimension selection and diagonal augmentation, outperforming naive methods in connectomics and graph population studies.

Findings

Low-rank methods outperform sample mean in small samples.

The approach yields eigen-connectomes correlating with brain structures.

The method shows significant improvements on human connectome data.

Abstract

In statistical connectomics, the quantitative study of brain networks, estimating the mean of a population of graphs based on a sample is a core problem. Often, this problem is especially difficult because the sample or cohort size is relatively small, sometimes even a single subject. While using the element-wise sample mean of the adjacency matrices is a common approach, this method does not exploit any underlying structural properties of the graphs. We propose using a low-rank method which incorporates tools for dimension selection and diagonal augmentation to smooth the estimates and improve performance over the naive methodology for small sample sizes. Theoretical results for the stochastic blockmodel show that this method offers major improvements when there are many vertices. Similarly, we demonstrate that the low-rank methods outperform the standard sample mean for a variety of independent edge distributions as well as human connectome data derived from magnetic resonance imaging, especially when sample sizes are small. Moreover, the low-rank methods yield "eigen-connectomes", which correlate with the lobe-structure of the human brain and superstructures of the mouse brain. These results indicate that low-rank methods are an important part of the tool box for researchers studying populations of graphs in general, and statistical connectomics in particular.